A quantile regression approach to define optimal ecological niche of cockle populations (Cerastoderma edule)

SUPPLEMENTARY DATA
Author

Amélie Lehuen, Chloé Dancie, Florent Grasso, Sven Smolders, Francesco Cozzoli, Francis Orvain

Published

August 11, 2024

1 Introduction

2 Materials and Methods

All data processing was conducted in R version 4.3.0 (2023-04-21 ucrt) except for MARS 3D pre-treatment in Matlab 2019a.

2.1 Study area

SuppFig 2.A: Maps of habitats areas defined in the study area. Dots represent the location of the biological samples

3 Results

3.1 Description of the biological data set

Biological data for C. edule comprised a total of n= 543 observations. The observations were split into periods as 2000-2005 - n= 108, 2006-2010 - n= 155, 2011-2015 - n= 174, 2015-2019 - n= 106. The following treatment only focussed on the mudflats used by C. edule: South Mudflat - n= 218, North Median Mudflat - n= 198, North Downstream Mudflat - n= 82, North Upstream Mudflat - n= 2.

SuppFig 3.A: C. edule population biomass [gAFDW/m²] and density [ind/m²] in the Seine estuary, by period for each area

3.2 Selection of the Hydro-Morpho-Sedimentary factors and their association

SuppFig 3.B: Mars3D selected factors maps in the Seine estuary

SuppFig 3.C: Mars3D selected factors means by areas and periods in the Seine estuary

SuppFig 3.D: Plot of the eigenvalues of principal components analysis made on abiotic factors.

SuppFig 3.E: PCA variable correlation plot with the abiotic factors’ contributions in bar plots for each axis. The red dotted line represents the mean contribution for all factors.

SuppFig 3.F: PCA variable correlation plot with the abiotic factors’ contributions in bar plots for each axis. The red dotted line represents the mean contribution for all factors.
SuppTab 3.A:

PCA scores for abiotic factors.
PCA results
Abiotic variables
Variable Cos2 Contrib
PC1 PC2 PC3 PC1 PC2 PC3
inundation time 0.07 0.67 0.00 1.67 23.10 0.13
current speed 0.72 0.05 0.01 17.82 1.86 0.46
daily maximum current speed 0.79 0.00 0.01 19.65 0.02 0.42
salinity 0.27 0.41 0.03 6.71 14.04 1.23
daily salinity range 0.72 0.09 0.00 17.78 3.02 0.13
temperature 0.07 0.24 0.02 1.83 8.31 1.00
daily temperature range 0.00 0.59 0.01 0.01 20.44 0.52
SPM 0.37 0.01 0.13 9.18 0.24 5.68
bathymetry 0.01 0.58 0.13 0.28 19.88 5.66
yearly sediment budget 0.00 0.16 0.01 0.00 5.47 0.38
bed shear stress 0.35 0.04 0.40 8.68 1.35 17.99
daily maximum bed shear stress 0.44 0.04 0.16 10.88 1.36 7.25
sediment total concentration 0.10 0.02 0.67 2.51 0.60 30.19
mud content 0.12 0.01 0.64 3.00 0.31 28.96

3.3 Model selection and validation

SuppTab 3.B:

AICc comparison for all SDMs computed, according to the quantile, the type of model and the response.
Biomass (gAFDW/m²) Density (ind/m²)
0.5 0.9 0.95 0.975 0.5 0.9 0.95 0.975
daily maximum current speed (m.s-1) & inundation time (%) & mud content (%)
Quantile regression bSpline 3745.4 4790.6 5148.1 5496.5 6758.8 7794.7 8126.5 8283.2
Quantile regression gaussian 3733.7 4746.8 5071.5 5418.7 6745.2 7819.8 8186.1 8533.3
Quantile regression linear 3757.0 4794.8 5162.0 5527.7 6767.1 7815.0 8142.6 8361.2
daily maximum current speed (m.s-1) & daily salinity range (u.s.i) & inundation time (%)
Quantile regression bSpline 3858.7 4933.4 5297.1 5668.9 6977.6 8065.7 8403.0 8634.6
Quantile regression gaussian 3835.0 4871.2 5240.9 5655.3 6969.1 8102.2 8476.1 8783.3
Quantile regression linear 3869.9 4918.5 5292.3 5702.6 6985.0 8067.4 8404.4 8706.1

Modelled vs observed biomass data plotted for each model functions. The black line represents the 1:1 ratio, quantiles 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.

Modelled vs observed biomass data plotted for each model functions. The black line represents the 1:1 ratio, quantiles 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.

3.4 Optimal Ecological Niche

3.4.1 Quantile Regression with gaussian equation

Gaussian SDM equation

Response_τ = A.e^{-[\frac{(Predictor1-μ1_τ)^2}{(2.σ1_τ^2)}~~+~~ \frac{(Predictor2-μ2_τ)^2}{(2.σ2_τ^2)}~~ +~~ \frac{(Predictor3-μ3_τ)^2}{(2.σ3_τ^2)}] }

SuppTab 3.C:

Coefficient of the models computed with gaussian equation (Equation 1), by quantile and response.
tau Biomass (gAFDW/m²) Density (ind/m²)
A μ 1 μ 2 μ 3 σ 1 σ 2 σ 3 A μ 1 μ 2 μ 3 σ 1 σ 2 σ 3
daily maximum current speed (m.s-1) * daily salinity range (u.s.i) * inundation time (%)
0.50 41.55 −2.89 4.26 0.85 1.84 3.51 0.13 9,509.94 −2.24 5.94 0.81 0.93 3.57 0.18
0.90 716.49 −1.87 1.87 0.97 1.04 5.18 0.22 2,686.24 0.17 4.37 0.95 0.31 4.41 0.21
0.95 392.63 −0.26 −4.40 1.22 0.58 8.40 0.34 113,728.75 0.39 5.24 3.30 0.24 3.62 0.86
0.97 3,464.31 0.49 3.27 2.69 0.19 3.79 0.69 421,906.57 0.48 −21.93 2.95 0.19 14.63 0.80
daily maximum current speed (m.s-1) * inundation time (%) * mud content (%)
0.50 80.54 −3.06 0.86 −0.28 1.56 0.15 0.71 292.75 0.33 0.79 0.27 0.19 0.17 0.35
0.90 1,321.22 −1.76 1.03 0.25 0.90 0.26 0.23 7,495.16 0.42 2.26 0.43 0.20 0.86 0.27
0.95 491.99 −0.17 1.22 0.30 0.50 0.34 0.18 85,227.47 0.46 4.01 0.62 0.20 1.20 0.48
0.97 272.78 0.43 1.15 0.30 0.25 0.30 0.20 151,774.30 0.50 4.77 0.41 0.21 1.40 0.32

Gaussian SDM plots

daily maximum current speed (m.s-1) & daily salinity range (u.s.i) & inundation time (%)

  1. Model optimum was 166.54 gAFDW/m² at 0.48 m.s-1, 3.16 and 100 %.

  2. Model optimum was 6661.38 ind/m² at 0.48 m.s-1, 0.2 and 100 %.

Model daily maximum current speed (m.s-1) & daily salinity range & inundation time (%) projection on the three abiotic factor axes and the predicted/observed validation plot associated. Black dots represents the observed data; lines the model; Coloured dots correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.Model daily maximum current speed (m.s-1) & daily salinity range & inundation time (%) projection on the three abiotic factor axes and the predicted/observed validation plot associated. Black dots represents the observed data; lines the model; Coloured dots correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.

Model daily maximum current speed (m.s-1) & daily salinity range & inundation time (%) projection on the three abiotic factor axes and the predicted/observed validation plot associated. Black dots represents the observed data; lines the model; Coloured dots correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.Model daily maximum current speed (m.s-1) & daily salinity range & inundation time (%) projection on the three abiotic factor axes and the predicted/observed validation plot associated. Black dots represents the observed data; lines the model; Coloured dots correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.

daily maximum current speed (m.s-1) & inundation time (%) & mud content (%)

  1. Model optimum was 239.48 gAFDW/m² at 0.43 m.s-1, 316 % and 0.31 %.

  2. Model optimum was 4036.77 ind/m² at 0.51 m.s-1,316 % and 0.41 %.

Model daily maximum current speed (m.s-1) & inundation time (%) & mud content (%) projection on the three abiotic factor axes and the predicted/observed validation plot associated. Black dots in A1 and B1 represents the observed data; lines the model; Coloured dots in A2 and B2 correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.Model daily maximum current speed (m.s-1) & inundation time (%) & mud content (%) projection on the three abiotic factor axes and the predicted/observed validation plot associated. Black dots in A1 and B1 represents the observed data; lines the model; Coloured dots in A2 and B2 correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.

Model daily maximum current speed (m.s-1) & inundation time (%) & mud content (%) projection on the three abiotic factor axes and the predicted/observed validation plot associated. Black dots in A1 and B1 represents the observed data; lines the model; Coloured dots in A2 and B2 correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.Model daily maximum current speed (m.s-1) & inundation time (%) & mud content (%) projection on the three abiotic factor axes and the predicted/observed validation plot associated. Black dots in A1 and B1 represents the observed data; lines the model; Coloured dots in A2 and B2 correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.

3.4.2 Application on Seine estuary

SDM models applied on the Seine estuary over the five periods in suitability index.

SDM models applied on the Seine estuary over the five periods in potential biomass.

Suitability index

Abiotic factors and resulting model at 97.5th centile suitability index per period and per area for all SDM models with a 95% confidence interval.

Abiotic factors and resulting model at 97.5th centile suitability index per period and per area for all SDM models with a 95% confidence interval.

3.4.3 Seine model applied to Schelde data

daily maximum current speed (m.s-1) & daily salinity range (u.s.i) & inundation time (%)

Model daily maximum current speed (m.s-1) & daily salinity range & inundation time (%) projection on the three abiotic factor axes with data from Schelde estuary in green dots, and the predicted/observed validation plot associated. Black dots represents the observed data; lines the model; Coloured dots correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.Model daily maximum current speed (m.s-1) & daily salinity range & inundation time (%) projection on the three abiotic factor axes with data from Schelde estuary in green dots, and the predicted/observed validation plot associated. Black dots represents the observed data; lines the model; Coloured dots correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.

Model daily maximum current speed (m.s-1) & daily salinity range & inundation time (%) projection on the three abiotic factor axes with data from Schelde estuary in green dots, and the predicted/observed validation plot associated. Black dots represents the observed data; lines the model; Coloured dots correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.Model daily maximum current speed (m.s-1) & daily salinity range & inundation time (%) projection on the three abiotic factor axes with data from Schelde estuary in green dots, and the predicted/observed validation plot associated. Black dots represents the observed data; lines the model; Coloured dots correspond to each decile of the modelled distribution and its corresponding observed, black line represents the 1:1 ratio. Quantiles are colour coded as 0,5 in blue, 0.9 in green, 0.95 in orange and 0.975 in red.

4 Supplementary data

4.1 Session information

─ Session info ───────────────────────────────────────────────────────────────
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The Scientific colour map batlow (Crameri 2018) is used in this study to prevent visual distortion of the data and exclusion of readers with colour­vision deficiencies (Crameri, Shephard, and Heron 2020).

References

Crameri, Fabio, Grace E. Shephard, and Philip J. Heron. 2020. “The Misuse of Colour in Science Communication.” Nature Communications 11 (1): 5444. https://doi.org/10.1038/s41467-020-19160-7.